考虑P-Δ效应的结构地震倒塌及影响因素分析
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摘要
P-Δ效应是引起结构在地震作用下倒塌的主要原因之一。以钢框架结构为研究对象,采用增量动力分析法(IDA)和推覆法(Pushover)分析了结构在考虑P-Δ效应时的地震响应特征。结果显示:考虑P-Δ效应后,结构的整体刚度降低,结构下部较容易出现动力失稳,而上部经历卸载,层间位移较小;由于几何非线性与材料非线性的共同作用,骨架曲线会产生明显的负刚度;对具有负刚度的骨架曲线,用三段折线模型进行简化更为合适。基于完全弹塑性滞回模型,研究了不同骨架曲线参数对结构抗倒塌能力的影响。结果表明:二阶效应系数增大,结构发生倒塌的概率增加,而名义延性系数和屈服后刚度比增大则会使结构的抗倒塌能力增强。
P-Δ effect is one of the crucial reasons causing the collapse of the structure under earthquake excitations.The response characteristic of the steel frame with P-Δ effect under strong earthquakes is researched in this paper.The numerical example shows that the stiffness of the structure decreases when the P-Δ effect is considered,and the lower stories of the structure are prone to dynamic instability,while the upper stories experience unloading and the interstory drifts are small.Due to the combination of the geometric nonlinearity and the material nonlinearity,the backbone curve is easier to behave a conspicuous negative slope,and the simplified trilinear curve is more appropriate than the bilinear curve to fit the original backbone curve with a descending segment.On the basis of the full elasto-plastic hysteretic model,the influences of the parameters of the backbone curve on the collapse resistance capacity of the structure are analyzed.The results demonstrate that the probability of the collapse becomes large as the second-order effect coefficient increases,while the increase of the nominal ductility factor and the post-yield stiffness ratio leads to the improvement of the collapse resistance capacity of the structure.
P-Δ effect is one of the crucial reasons causing the collapse of the structure under earthquake excitations.The response characteristic of the steel frame with P-Δ effect under strong earthquakes is researched in this paper.The numerical example shows that the stiffness of the structure decreases when the P-Δ effect is considered,and the lower stories of the structure are prone to dynamic instability,while the upper stories experience unloading and the interstory drifts are small.Due to the combination of the geometric nonlinearity and the material nonlinearity,the backbone curve is easier to behave a conspicuous negative slope,and the simplified trilinear curve is more appropriate than the bilinear curve to fit the original backbone curve with a descending segment.On the basis of the full elasto-plastic hysteretic model,the influences of the parameters of the backbone curve on the collapse resistance capacity of the structure are analyzed.The results demonstrate that the probability of the collapse becomes large as the second-order effect coefficient increases,while the increase of the nominal ductility factor and the post-yield stiffness ratio leads to the improvement of the collapse resistance capacity of the structure.
引文
[1]Zareian F,Krawinkler H.Assessment of probability ofcollapse and design for collapse safety[J].EarthquakeEngineering&Structure Dynamics,2007,36(13):1901-1914.
[2]Lignos D G,Krawinkler H,Whittaker A S.Predictionand validation of sidesway collapse of two scale modelsof a 4-story steel moment frame[J].EarthquakeEngineering&Structural Dynamics,2011,40(7):807-825.
[3]叶列平,曲哲,陆新征,等.提高建筑结构抗地震倒塌能力的设计思想与方法[J].建筑结构学报,2008,29(4):42-50.(YE Lieping,QU Zhe,LUXinzheng,et al.Collapse prevention of buildingstructures:a lesson from the Wenchuan Earthquake[J].Journal of Building Structures,2008,29(4):42-50.(in Chinese))
[4]吕大刚,于晓辉,陈志恒.钢筋混凝土框架结构侧向倒塌地震易损性分析[J].哈尔滨工业大学学报,2011,43(6):1-5.(LüDagang,Yu Xiaohui,ChenZhiheng.Lateral seismic collapse fragility analysis ofRC frame structures[J].Journal of Harbin Institute ofTechnology,2011,43(6):1-5.(in Chinese))
[5]Vamvatsikos D,Cornell C A.Incremental dynamicanalysis[J].Earthquake Engineering&StructuralDynamics,2002,31(3):491-514.
[6]Vamvatsikos D,Cornell C A.Direct estimation ofseismic demand and capacity of multidegree-of-freedomsystems through incremental dynamic analysis of singledegree of freedom approximation[J].Journal ofStructural Engineering,ASCE,2005,131(4):589-599.
[7]Dolsek M,Fajfar P.IN2-a simple alternative for IDA[C]//Proceedings of the 13th World Conference onEarthquake Engineering.Paper No.3353.Ottawa,Canada:The Canadian Association for EarthquakeEngineering,2004.
[8]Han S W,Chopra A K.Approximate incrementaldynamic analysis using the modal pushover analysisprocedure[J].Earthquake Engineering&StructuralDynamics,2006,35(15):1853-1873.
[9]吴京,梁仁杰,王春林,等.基于非线性静力分析的地震强度直接计算方法[J].建筑结构学报,2011,32(9):44-49.(WU Jing,LIANG Renjie,WANGChunlin,et al.Direct calculation of seismic intensitybased on non-linear static analysis[J].Journal ofBuilding Structures,2011,32(9):44-49.(inChinese))
[10]Han S W,Moon K H,Chopra A K.Application ofMPA to estimate probability of collapse of structures[J].Earthquake Engineering&Structural Dynamics,2010,39(11):1259-1278.
[11]Bernal D.Amplication factors for inelastic dynamic P-Δeffects in earthquake analysis[J].EarthquakeEngineering&Structural Dynamics,1987,15(5):635-651.
[12]Ibarra L F,Krawinkler H.Variance of collapsecapacity of SDOF systems under earthquake excitations[J].Earthquake Engineering&Structural Dynamics,2011,40(12):1299-1314.
[13]Black E F.Use of stability coefficients for evaluatingthe P-Δeffect in regular steel moment resisting frames[J].Engineering Structures,2011,33(4):1205-1216.
[14]杜修力,李小军,尹之潜.极限后负刚度模型对RC框架结构地震倒塌反应的影响[J].计算结构力学及其应用,1993,10(2):179-186.(Du Xiuli,LiXiaojun,Yin Zhiqian.The influence of restoring forcemodel with post-ultimate negative stiffness onearthquake collapse response of RC frame structures[J].Computational Structural Mechanics andApplications,1993,10(2):179-186.(in Chinese))
[15]童根树,赵永峰.动力P-Δ效应对地震力调整系数的影响[J].浙江大学学报:工学版,2007,41(1):120-125.(Tong Genshu,Zhao Yongfeng.DynamicP-Δeffects on seismic force modification factors[J].Journal of Zhejiang University:Engineering Science,2007,41(1):120-125.(in Chinese))
[16]翟长海,孙亚民,谢礼立.考虑P-Δ效应的等延性位移比谱[J].哈尔滨工业大学学报,2007,39(10):1513-1516.(Zhai Changhai,Sun Yamin,XieLili.Estimation of P-Δeffect on constant-ductilityinelastic displacement ratio spectra[J].Journal ofHarbin Institute of Technology,2007,39(10):1513-1516.(in Chinese))
[17]魏斌,李建中,蒋娜芳.考虑P-Δ效应的桥梁地震反应分析与设计[J].地震工程与工程振动,2010,30(3):129-135.(Wei Bin,Li Jianzhong,JiangNafang.Seismic analysis and design of bridge piersconsidering P-Δeffects[J].Journal of EarthquakeEngineering and Engineering Vibration,2010,30(3):129-135.(in Chinese))
[18]Miranda E.Evaluation of site-dependent inelasticseismic design spectra[J].Journal of StructuralEngineering,ASCE,1993,119(5):1319-1338.
[2]Lignos D G,Krawinkler H,Whittaker A S.Predictionand validation of sidesway collapse of two scale modelsof a 4-story steel moment frame[J].EarthquakeEngineering&Structural Dynamics,2011,40(7):807-825.
[3]叶列平,曲哲,陆新征,等.提高建筑结构抗地震倒塌能力的设计思想与方法[J].建筑结构学报,2008,29(4):42-50.(YE Lieping,QU Zhe,LUXinzheng,et al.Collapse prevention of buildingstructures:a lesson from the Wenchuan Earthquake[J].Journal of Building Structures,2008,29(4):42-50.(in Chinese))
[4]吕大刚,于晓辉,陈志恒.钢筋混凝土框架结构侧向倒塌地震易损性分析[J].哈尔滨工业大学学报,2011,43(6):1-5.(LüDagang,Yu Xiaohui,ChenZhiheng.Lateral seismic collapse fragility analysis ofRC frame structures[J].Journal of Harbin Institute ofTechnology,2011,43(6):1-5.(in Chinese))
[5]Vamvatsikos D,Cornell C A.Incremental dynamicanalysis[J].Earthquake Engineering&StructuralDynamics,2002,31(3):491-514.
[6]Vamvatsikos D,Cornell C A.Direct estimation ofseismic demand and capacity of multidegree-of-freedomsystems through incremental dynamic analysis of singledegree of freedom approximation[J].Journal ofStructural Engineering,ASCE,2005,131(4):589-599.
[7]Dolsek M,Fajfar P.IN2-a simple alternative for IDA[C]//Proceedings of the 13th World Conference onEarthquake Engineering.Paper No.3353.Ottawa,Canada:The Canadian Association for EarthquakeEngineering,2004.
[8]Han S W,Chopra A K.Approximate incrementaldynamic analysis using the modal pushover analysisprocedure[J].Earthquake Engineering&StructuralDynamics,2006,35(15):1853-1873.
[9]吴京,梁仁杰,王春林,等.基于非线性静力分析的地震强度直接计算方法[J].建筑结构学报,2011,32(9):44-49.(WU Jing,LIANG Renjie,WANGChunlin,et al.Direct calculation of seismic intensitybased on non-linear static analysis[J].Journal ofBuilding Structures,2011,32(9):44-49.(inChinese))
[10]Han S W,Moon K H,Chopra A K.Application ofMPA to estimate probability of collapse of structures[J].Earthquake Engineering&Structural Dynamics,2010,39(11):1259-1278.
[11]Bernal D.Amplication factors for inelastic dynamic P-Δeffects in earthquake analysis[J].EarthquakeEngineering&Structural Dynamics,1987,15(5):635-651.
[12]Ibarra L F,Krawinkler H.Variance of collapsecapacity of SDOF systems under earthquake excitations[J].Earthquake Engineering&Structural Dynamics,2011,40(12):1299-1314.
[13]Black E F.Use of stability coefficients for evaluatingthe P-Δeffect in regular steel moment resisting frames[J].Engineering Structures,2011,33(4):1205-1216.
[14]杜修力,李小军,尹之潜.极限后负刚度模型对RC框架结构地震倒塌反应的影响[J].计算结构力学及其应用,1993,10(2):179-186.(Du Xiuli,LiXiaojun,Yin Zhiqian.The influence of restoring forcemodel with post-ultimate negative stiffness onearthquake collapse response of RC frame structures[J].Computational Structural Mechanics andApplications,1993,10(2):179-186.(in Chinese))
[15]童根树,赵永峰.动力P-Δ效应对地震力调整系数的影响[J].浙江大学学报:工学版,2007,41(1):120-125.(Tong Genshu,Zhao Yongfeng.DynamicP-Δeffects on seismic force modification factors[J].Journal of Zhejiang University:Engineering Science,2007,41(1):120-125.(in Chinese))
[16]翟长海,孙亚民,谢礼立.考虑P-Δ效应的等延性位移比谱[J].哈尔滨工业大学学报,2007,39(10):1513-1516.(Zhai Changhai,Sun Yamin,XieLili.Estimation of P-Δeffect on constant-ductilityinelastic displacement ratio spectra[J].Journal ofHarbin Institute of Technology,2007,39(10):1513-1516.(in Chinese))
[17]魏斌,李建中,蒋娜芳.考虑P-Δ效应的桥梁地震反应分析与设计[J].地震工程与工程振动,2010,30(3):129-135.(Wei Bin,Li Jianzhong,JiangNafang.Seismic analysis and design of bridge piersconsidering P-Δeffects[J].Journal of EarthquakeEngineering and Engineering Vibration,2010,30(3):129-135.(in Chinese))
[18]Miranda E.Evaluation of site-dependent inelasticseismic design spectra[J].Journal of StructuralEngineering,ASCE,1993,119(5):1319-1338.
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